Quantum Geometry Matrix Theory and Gravity

Building on mathematical structures familiar from quantum mechanics this book provides an introduction to quantization in a broad context before developing a framework for quantum geometry in Matrix Theory and string theory. Taking a physics-oriented approach to quantum geometry this framework helps explain the physics of YangMills-type matrix models leading to a quantum theory of space-time and matter. This novel framework is then applied to Matrix Theory which is defined through distinguished maximally supersymmetric matrix models related to string theory. A mechanism for gravity is discussed in depth which emerges as a quantum effect on quantum space-time within Matrix Theory. Using explicit examples and exercises readers will develop a physical intuition for the mathematical concepts and mechanisms. It will benefit advanced students and researchers in theoretical and mathematical physics and is a useful resource for physicists and mathematicians interested in the geometrical aspects of quantization in a broader context.